Simultaneously see Eevee and Cycles renderings
Maybe an old question but worth mentioning that YES, it is indeed possible. Though may be seen as a workaround:
First place all your settings as you'd like them with Eevee set as your renderer. This includes activating AO, screenspace reflections, irradiance/reflection objects etc. Any setting that is relevant to Eevee basically. This doesn't include lights.
NOTE: HDRI will be independant from Cycles world settings if you're using an irradiance object to bake the lighting.
When you have it all set, split the window to have a second 3D view, then switch to Cycles as your renderer. In the one view set the shading mode to rendered (shortcut: Z) which will be Cycles, and set the other shading mode to material preview for Eevee.
In the material preview window, make sure that the extra options &quot;Scene lights&quot; and &quot;Scene world&quot; are checked.